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Ann. Geophys., 23, 2589-2597, 2005
www.ann-geophys.net/23/2589/2005/
© European Geosciences Union 2005
Relation between magnetic fields and electric currents in plasmas
V. M. Vasyliunas
Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany
Abstract. Maxwell's equations allow the magnetic field B
to be calculated if the electric current density
J is assumed to be completely known as
a function of space and time. The charged particles
that constitute the current, however, are subject to
Newton's laws as well, and J can be changed
by forces acting on charged particles. Particularly
in plasmas, where the concentration of charged particles
is high, the effect of the electromagnetic field
calculated from a given J on J itself
cannot be ignored. Whereas in ordinary laboratory physics
one is accustomed to take J as primary and
B as derived from J, it is often asserted that
in plasmas B should be
viewed as primary and J as derived from B simply
as (c/4π)∇×B.
Here I investigate the relation between
∇×B and J in the same terms
and by the same method as previously applied to the MHD
relation between the electric field and the plasma bulk flow
vmv2001: assume that one but not the other
is present initially, and calculate what happens. The result
is that, for
configurations with spatial scales much larger than the
electron inertial length λe, a given ∇×B
produces the corresponding J, while a given
J does not produce any ∇×B but
disappears instead. The reason for this can be understood by noting that
∇×B≠4π/c)J
implies a time-varying electric field (displacement current)
which acts to change both terms (in order to bring them toward equality);
the changes in the two terms, however, proceed on different time scales,
light travel time for B and electron plasma period for J,
and clearly the term changing much more slowly is the one that survives.
(By definition,
the two time scales are equal at λe.)
On larger scales, the evolution of B (and hence also
of ∇×B) is governed by ∇×E,
with E determined by plasma dynamics via the generalized Ohm's law;
as illustrative simple examples, I discuss the formation of magnetic drift
currents in the magnetosphere and of Pedersen and Hall currents in the
ionosphere.
Keywords. Ionosphere (Electric fields and currents) –
Magnetospheric physics (Magnetosphere-ionosphere interactions)
– Space plasma physics (Kinetic and MHD theory)
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